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This is an old revision of this page, as edited by Paul August (talk | contribs) at 06:24, 17 February 2005 (→03D20 Recursive functions and relations, subrecursive hierarchies). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

This page provides a list of all articles available at PlanetMath in the following topic:

03-XX Mathematical logic and foundations.

This list will be periodically updated. Each entry in the list has three fields:

  1. PM : The first field is the link to the PlanetMath article, along with the article's object ID.
  2. WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
  3. Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:
Status means PM article
N not needed
A adequately covered
C copied
M merged
NC needs copying
NM needs merging
  • Please update the WP and Status fields as appropriate.
  • if the WP field is correct please remove the qualifier "guess".
  • If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
  • If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
  • If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.

Don't forget to include the relevant template if you copy over text or feel like an external link is warranted

  • {{planetmath|id=|title=}} for copied over text
  • {{planetmath reference|id=|title=}} for an external link

See the main page for examples and usage criteria.

One can use the web-based program Pmform to convert PlanetMath articles to the Wikipedia format. As a side benefit, this tool will place the PlanetMath template for you.

03-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

Needs to be merged: 7. Paul August ☎ 05:25, Feb 16, 2005 (UTC)
Needs to be copied: 2. Paul August ☎ 05:25, Feb 16, 2005 (UTC)
Needs to be reviewed: 3. Paul August ☎ 05:25, Feb 16, 2005 (UTC)
Copied the section "Colloquial Usage" from PM into WP article. Paul August ☎ 20:37, Feb 4, 2005 (UTC)
Paul August ☎ 15:03, Feb 2, 2005 (UTC)
Paul August ☎ 15:22, Feb 2, 2005 (UTC)
Actually the PM article is misnamed, it is really about "Cantor's Theorem". WP does not have an article about "Cantor's Paradox" but should. Paul August ☎ 02:21, Feb 3, 2005 (UTC)
Paul August ☎ 02:25, Feb 3, 2005 (UTC)
Paul August ☎ 02:43, Feb 3, 2005 (UTC)
This PM article is really about what WP calls an indicator function not what WP calls a characteristic function which is a different thing. The PM article gives a fomula for the indicator function of the symetric difference of two sets and for the complement of a set, which could be merged with the WP article. Paul August ☎ 19:59, Feb 5, 2005 (UTC)
Paul August ☎ 03:08, Feb 3, 2005 (UTC)
Paul August ☎ 03:15, Feb 3, 2005 (UTC)
"Cycle" is defined in Permutation but it should probably have its own article. Paul August ☎ 04:17, Feb 16, 2005 (UTC)
Paul August ☎ 00:08, Feb 4, 2005 (UTC)
Paul August ☎ 00:10, Feb 4, 2005 (UTC)
Paul August ☎ 00:22, Feb 4, 2005 (UTC)
Paul August ☎ 00:22, Feb 4, 2005 (UTC)
Paul August ☎ 03:49, Feb 4, 2005 (UTC)
Paul August ☎ 03:49, Feb 4, 2005 (UTC)
PM article gives a definition of the integers as an equivalence class on NxN. Also conntains some additional algebraic properties: integral domain, ordered ring, valuation. Paul August ☎ 03:49, Feb 4, 2005 (UTC)
I would say this should go in a separate article, called say construction of integers. This in order to keep the integer page elementary. We will discuss this more. Oleg Alexandrov | talk 20:36, 5 Feb 2005 (UTC)
Paul August ☎ 04:07, Feb 4, 2005 (UTC)
Paul August ☎ 04:10, Feb 16, 2005 (UTC)
Paul August ☎ 04:16, Feb 4, 2005 (UTC)
Paul August ☎ 04:32, Feb 4, 2005 (UTC)
Paul August ☎ 04:32, Feb 4, 2005 (UTC)
Paul August ☎ 04:32, Feb 4, 2005 (UTC)
Paul August ☎ 20:37, Feb 4, 2005 (UTC)
Paul August ☎ 20:57, Feb 4, 2005 (UTC)
Paul August ☎ 04:27, Feb 16, 2005 (UTC)
Paul August ☎ 22:51, Feb 4, 2005 (UTC)
Paul August ☎ 22:08, Feb 5, 2005 (UTC)
The PM article contains a proposition and proof about the "signature of a permutation" which me may or may not want to include. Paul August ☎ 21:07, Feb 5, 2005 (UTC)
The most general definition of simple function is a finite linear combination of indicator functions — the MP defines it only in the context of a "measurable space". I think the (more general) definition should be merged into indicator function, but I suppose, it could have its own article: Simple function. For its use in Measure theory, see for example: Lebesgue integration and Lebesgue-Stieltjes integration. Paul August ☎ 18:29, Feb 14, 2005 (UTC)
  • PM: subset, id=472 -- WP: subset -- Status: WP article more complete
Paul August ☎ 03:58, Feb 5, 2005 (UTC)
Paul August ☎ 03:58, Feb 5, 2005 (UTC)
Actually Transposition (mathematics) is just a redirect to symmetric group, but I think it should have its own article. Paul August ☎ 19:08, Feb 14, 2005 (UTC)
Paul August ☎ 03:58, Feb 5, 2005 (UTC)

03A05 Philosophical and critical

Needs to be reviewed: 1 Paul August ☎ 05:29, Feb 16, 2005 (UTC)

03B05 Classical propositional logic

Needs to be merged: 1. Paul August ☎ 20:37, Feb 16, 2005 (UTC)
Needs to be reviewed: 3. Paul August ☎ 20:37, Feb 16, 2005 (UTC)
See 01A20 Greek, Roman
PM article is essentially empty. Paul August ☎ 03:50, Feb 6, 2005 (UTC)
Paul August ☎ 03:55, Feb 6, 2005 (UTC)
Paul August ☎ 04:56, Feb 6, 2005 (UTC)
Paul August ☎ 05:01, Feb 6, 2005 (UTC)
The PM article is empty. Paul August ☎ 05:10, Feb 6, 2005 (UTC)
Paul August ☎ 05:28, Feb 6, 2005 (UTC)
Paul August ☎ 05:34, Feb 6, 2005 (UTC)
Paul August ☎ 18:39, Feb 14, 2005 (UTC)

03B10 Classical first-order logic

Needs to be merged: 3. Paul August ☎ 20:44, Feb 16, 2005 (UTC)
Needs to be reviewed: 33. Paul August ☎ 20:44, Feb 16, 2005 (UTC)
Paul August ☎ 18:33, Feb 6, 2005 (UTC)
  • PM: Boolean, id=543 -- WP: Boolean -- Status: WP article more complete
Paul August ☎ 20:37, Feb 6, 2005 (UTC)
Paul August ☎ 21:17, Feb 16, 2005 (UTC)
Paul August ☎ 21:36, Feb 16, 2005 (UTC)
  • PM: theory, id=3383 -- Duplicate entry.
See 03B05 Classical propositional logic
Paul August ☎ 03:54, Feb 13, 2005 (UTC)

03B15 Higher-order logic and type theory

Needs to be merged: 1. Paul August ☎ 05:17, Feb 17, 2005 (UTC)
Needs to be reviewed: 4. Paul August ☎ 05:17, Feb 17, 2005 (UTC)
See 03B10 Classical first-order logic
  • PM: logic, id=3380 -- Duplicate entry.
See 03B10 Classical first-order logic
See 03B10 Classical first-order logic
See 03B10 Classical first-order logic
Paul August ☎ 05:17, Feb 17, 2005 (UTC)
See 03B10 Classical first-order logic

03B40 Combinatory logic and lambda-calculus

Needs to be merged: 2. Paul August ☎ 04:50, Feb 17, 2005 (UTC)
Paul August ☎ 04:50, Feb 17, 2005 (UTC)
Paul August ☎ 04:45, Feb 17, 2005 (UTC)
Paul August ☎ 21:08, Feb 16, 2005 (UTC)

03B48 Probability and inductive logic

Needs to be merged: 1. Paul August ☎ 04:51, Feb 17, 2005 (UTC)
Paul August ☎ 04:10, Feb 13, 2005 (UTC)
Paul August ☎ 04:04, Feb 13, 2005 (UTC)

03B50 Many-valued logic

All articles processed. Paul August ☎ 05:10, Feb 17, 2005 (UTC)
Apparently deleted. See also neutrosophic probability in 60A10 Probabilistic measure theory. Ben Cairns 06:10, 3 Feb 2005 (UTC).

03B53 Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.)

All articles processed. Paul August ☎ 05:11, Feb 17, 2005 (UTC)
See 03B50 Many-valued logic

03B60 Other nonclassical logic

All articles processed. Paul August ☎ 05:12, Feb 17, 2005 (UTC)
See 03B50 Many-valued logic

03B99 Miscellaneous

Needs to be reviewed: 8. Paul August ☎ 05:02, Feb 17, 2005 (UTC)
  • PM: axiom, id=3088 -- Duplicate entry.
See 03A05 Philosophical and critical

03C05 Equational classes, universal algebra

Needs to be reviewed: 6. Paul August ☎ 05:06, Feb 17, 2005 (UTC)

03C07 Basic properties of first-order languages and structures

Needs to be reviewed: 23. Paul August ☎ 05:21, Feb 17, 2005 (UTC)
See 03C05 Equational classes, universal algebra
See 03B10 Classical first-order logic
See 03B10 Classical first-order logic
See 03C05 Equational classes, universal algebra
See 03B10 Classical first-order logic
See 03B10 Classical first-order logic
See 03B10 Classical first-order logic
See 03C05 Equational classes, universal algebra
  • PM: kernel, id=4485 -- Duplicate entry.
See 03C05 Equational classes, universal algebra
See 03C05 Equational classes, universal algebra
See 03B10 Classical first-order logic
See 03B10 Classical first-order logic
See 03C05 Equational classes, universal algebra
See 03B10 Classical first-order logic
See 03B10 Classical first-order logic
  • PM: type, id=3913 -- WP guess: type -- Status:
All articles processed. Paul August ☎ 05:23, Feb 17, 2005 (UTC)
See 03C07 Basic properties of first-order languages and structures
See 03B10 Classical first-order logic
See 03C07 Basic properties of first-order languages and structures

03C15 Denumerable structures

Needs to be merged: 1. Paul August ☎ 05:27, Feb 17, 2005 (UTC)
Paul August ☎ 05:27, Feb 17, 2005 (UTC)

03C30 Other model constructions

All articles processed. Paul August ☎ 05:35, Feb 17, 2005 (UTC)
See 03C15 Denumerable structures

03C35 Categoricity and completeness of theories

Needs to be merged: 2. Paul August ☎ 05:42, Feb 17, 2005 (UTC)
Needs to be reviewed: 1. Paul August ☎ 05:42, Feb 17, 2005 (UTC)
Paul August ☎ 05:42, Feb 17, 2005 (UTC)
Paul August ☎ 05:42, Feb 17, 2005 (UTC)
All articles processed. Paul August ☎ 05:43, Feb 17, 2005 (UTC)
See 03C07 Basic properties of first-order languages and structures
See 03C07 Basic properties of first-order languages and structures
See 03C07 Basic properties of first-order languages and structures

03C50 Models with special properties (saturated, rigid, etc.)

Needs to be reviewed: 3. Paul August ☎ 05:46, Feb 17, 2005 (UTC)

03C52 Properties of classes of models

Needs to be reviewed: 1. Paul August ☎ 05:47, Feb 17, 2005 (UTC)
See 03C50 Models with special properties (saturated, rigid, etc.)
See 03C15 Denumerable structures
See 03C50 Models with special properties (saturated, rigid, etc.)

03C57 Effective and recursion-theoretic model theory

Needs to be reviewed: 1. Paul August ☎ 05:50, Feb 17, 2005 (UTC)

03C64 Model theory of ordered structures; o-minimality

Needs to be merged: 1. Paul August ☎ 05:57, Feb 17, 2005 (UTC)
Needs to be reviewed: 2. Paul August ☎ 05:57, Feb 17, 2005 (UTC)
Paul August ☎ 02:23, Feb 14, 2005 (UTC)

03C68 Other classical first-order model theory

Needs to be reviewed: 1. Paul August ☎ 05:58, Feb 17, 2005 (UTC)

03C80 Logic with extra quantifiers and operators

All articles processed. Paul August ☎ 05:58, Feb 17, 2005 (UTC)
See 03B10 Classical first-order logic

03C90 Nonclassical models (Boolean-valued, sheaf, etc.)

Needs to be reviewed: 1. Paul August ☎ 05:59, Feb 17, 2005 (UTC)

03C95 Abstract model theory

All articles processed. Paul August ☎ 06:00, Feb 17, 2005 (UTC)
See 03C68 Other classical first-order model theory

03C99 Miscellaneous

Needs to be merged: 5. Paul August ☎ 06:01, Feb 17, 2005 (UTC)
See 03B10 Classical first-order logic
Paul August ☎ 01:27, Feb 14, 2005 (UTC)
A bit of notation could be merged. Paul August ☎ 01:37, Feb 14, 2005 (UTC)
Paul August ☎ 01:53, Feb 14, 2005 (UTC)
Or perhaps it could be copied to say: Model (model theory). Paul August ☎ 01:58, Feb 14, 2005 (UTC)
Paul August ☎ 02:00, Feb 14, 2005 (UTC)
See 03B10 Classical first-order logic

03D05 Automata and formal grammars in connection with logical questions

Needs to be merged: 1. Paul August ☎ 19:58, Feb 16, 2005 (UTC)
See 03C57 Effective and recursion-theoretic model theory
Paul August ☎ 02:46, Feb 14, 2005 (UTC)
Needs to be merged: 4. Paul August ☎ 06:02, Feb 17, 2005 (UTC)
Paul August ☎ 02:34, Feb 14, 2005 (UTC)
Paul August ☎ 02:39, Feb 14, 2005 (UTC)
Paul August ☎ 03:08, Feb 14, 2005 (UTC)
Paul August ☎ 03:01, Feb 14, 2005 (UTC)

03D20 Recursive functions and relations, subrecursive hierarchies

Needs to be merged: 3. Paul August ☎ 06:24, Feb 17, 2005 (UTC)
Paul August ☎ 06:20, Feb 17, 2005 (UTC)
Paul August ☎ 06:24, Feb 17, 2005 (UTC)
Paul August ☎ 06:12, Feb 17, 2005 (UTC)
Paul August ☎ 06:18, Feb 17, 2005 (UTC)
Paul August ☎ 06:24, Feb 17, 2005 (UTC)

03D25 Recursively (computably) enumerable sets and degrees

03D75 Abstract and axiomatic computability and recursion theory

03E02 Partition relations

03E04 Ordered sets and their cofinalities; pcf theory

03E05 Other combinatorial set theory

03E10 Ordinal and cardinal numbers

  • PM: club, id=3227 -- WP guess: club -- Status:

03E15 Descriptive set theory

03E17 Cardinal characteristics of the continuum

See 03E10 Ordinal and cardinal numbers
See 03E10 Ordinal and cardinal numbers
See 03E10 Ordinal and cardinal numbers

03E20 Other classical set theory (including functions, relations, and set algebra)

See 03E04 Ordered sets and their cofinalities; pcf theory

03E30 Axiomatics of classical set theory and its fragments

See 03E25 Axiom of choice and related propositions
See 03E25 Axiom of choice and related propositions

03E35 Consistency and independence results

03E40 Other aspects of forcing and Boolean-valued models

See 03C90 Nonclassical models (Boolean-valued, sheaf, etc.)
See 03E35 Consistency and independence results
See 03E35 Consistency and independence results
See 03E35 Consistency and independence results
  • PM: forcing, id=3039 -- Duplicate entry.
See 03E35 Consistency and independence results
See 03E35 Consistency and independence results
See 03E35 Consistency and independence results
See 03E35 Consistency and independence results
See 03E35 Consistency and independence results
See 03E35 Consistency and independence results
See 03E35 Consistency and independence results

03E45 Inner models, including constructibility, ordinal definability, and core models

03E50 Continuum hypothesis and Martin's axiom

  • PM: forcing, id=3039 -- Duplicate entry.
See 03E35 Consistency and independence results

03E55 Large cardinals

03E65 Other hypotheses and axioms

03E70 Nonclassical and second-order set theories

Apparently a deleted article. See also neutrosophic probability in 60A10 Probabilistic measure theory. Ben Cairns 06:07, 3 Feb 2005 (UTC).

03E72 Fuzzy set theory

See 03E70 Nonclassical and second-order set theories

03E99 Miscellaneous

Paul August ☎ 04:21, Feb 13, 2005 (UTC)
Paul August ☎ 04:26, Feb 13, 2005 (UTC)
Paul August ☎ 04:30, Feb 13, 2005 (UTC)
Paul August ☎ 04:32, Feb 13, 2005 (UTC)
Paul August ☎ 04:38, Feb 13, 2005 (UTC)
Paul August ☎ 04:44, Feb 13, 2005 (UTC)
In fact the MP article should replace (almost) our article. Paul August ☎ 05:03, Feb 13, 2005 (UTC)
Paul August ☎ 05:22, Feb 13, 2005 (UTC)
Paul August ☎ 05:30, Feb 13, 2005 (UTC)
The more common term (in my experience) is "filter base".Paul August ☎ 21:08, Feb 14, 2005 (UTC)
Paul August ☎ 21:14, Feb 14, 2005 (UTC)
Paul August ☎ 21:22, Feb 14, 2005 (UTC)
Paul August ☎ 21:26, Feb 14, 2005 (UTC)
See 03E10 Ordinal and cardinal numbers
Paul August ☎ 21:30, Feb 14, 2005 (UTC)
Paul August ☎ 21:48, Feb 14, 2005 (UTC)
  • PM: set, id=1635 -- WP: set -- Status: WP article more complete
Paul August ☎ 22:09, Feb 14, 2005 (UTC)
  • PM: superset, id=2585 -- WP: subset -- Status: WP article more complete
Paul August ☎ 01:54, Feb 15, 2005 (UTC)
Paul August ☎ 02:00, Feb 15, 2005 (UTC)

03F03 Proof theory, general

See 03C07 Basic properties of first-order languages and structures
Paul August ☎ 02:11, Feb 15, 2005 (UTC)

03F07 Structure of proofs

See 03B48 Probability and inductive logic

03F15 Recursive ordinals and ordinal notations

See 03E10 Ordinal and cardinal numbers
See 03E10 Ordinal and cardinal numbers
See 03E10 Ordinal and cardinal numbers
See 03E10 Ordinal and cardinal numbers

03F20 Complexity of proofs

03F30 First-order arithmetic and fragments

  • PM: PA, id=3301 -- WP guess: PA -- Status:

03F35 Second- and higher-order arithmetic and fragments

  • PM: Z_2, id=3308 -- WP guess: Z_2 -- Status:

03F55 Intuitionistic mathematics

03F60 Constructive and recursive analysis

03G05 Boolean algebras

03G99 Miscellaneous

03H05 Nonstandard models in mathematics

See 03C64 Model theory of ordered structures; o-minimality
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