Wikipedia:Requested articles/Mathematics/Logic

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Model theory, proof theory, and recursion theory

• Definitions of infinity:

1. Equilateral_triangle#Circumradius,_inradius,_and_exradii

• Behavioral semantics - An axiomatic semantics of concurrent programming languages, (see Lamport 1985)
• Herbrand consistency - might be enough to explain this term in the consistency article.
• Homogeneous model - currently a redirect to Model theory
• Method of indicators - Model-theoretic method used to prove the Paris–Harrington theorem without diagonalization
• Proof identity - some references:

• Straßburger, Lutz (20 October 2006), "Proof Nets and the Identity of Proofs", Technical Report 6013, INRIA
• Kuznets, Roman (2007), "Proof Identity for Classical Logic: Generalizing to Normality", LFCS (PDF), pp. 332–348
• MO thread

• Proof minimization - including proof compression (i.e. algorithmic proof minimization) and open challenges like pmproofs

• The proof compression article only covers a tiny proportion / a special case.

• Subrecursion theory - The study of "levels of recursion", such as primitive recursion, double recursion and μ-recursive functions (noted by, for example: Rose, H.E., "Subrecursion: Functions and hierarchies", Oxford University Press, New York, USA, 1984. ISBN 0-19-853189-3). Possibly a foreshadowing to computational complexity theory.
• Predicative arithmetic - currently a redirect to Impredicativity
• Hyperhyperimmune set
• Hyperhypersimple set
• Regressive set
• Retraceable set
• Feferman-Levy model
• Simple theory - there are at least two textbooks:

• Wagner-, Frank, (2011). Simple theories. Springer. ISBN 978-90-481-5417-3.{{cite book}}: CS1 maint: extra punctuation (link) CS1 maint: multiple names: authors list (link)
• Kim, Byunghan (2013-10-17). Simplicity Theory. Oxford University Press. doi:10.1093/acprof:oso/9780198567387.001.0001.

Set theory

• C-measurable set
• Comprehensive set
• Canonical representative
• Extended set theory (D L Childs et al.)
• Paris model
• Quasi strategy - (Currently a redirect to an empty paragraph)
• Scott analysis (should also have redirects from Scott sentence and Scott rank)
• Unfolded Banach-Mazur game - Banach–Mazur game
• Weakly homogeneously Suslin set
• Yannakakis' algorithm

Relations

• Bichotomous relation
• Dichotomettic relation
• Trichotomous relation (currently a redirect to Law of trichotomy)
• Contact relation (currently a redirect to binary relation)
• Regular relation
• Normalizing relation
• Consistent relation
• Definite relation
• Weakly dense relation
• Determinant relation
• Terminating relation - (currently a redirect to abstract rewriting system)
• Convergent relation
• Orthogonal relation
• Rooted relation
• Transitively connected relation
• Deterministic relation
• Cyclical relation
• Weakly connected relation

Other

Requests listed in this section may belong somewhere else. Please help by moving them to a suitable location.

• Computational verb logic
• Countable language
• First-degree entailment
• Nominal logic - perhaps related to Nominal terms (computer science) and Nominal techniques, see also
• Nominal sets
• Order-sorted equational logic
• Propositional linear temporal logic
• Trivial truth - currently a redirect to Triviality; a previous comment stated: there is an article vacuous truth, and triviality but no article trivial truth, was thinking about making it an link to Tautology but then thought not all tautologies are trivial (obvious) truths, maybe P -> P is the only tautology that really is an trivial truth)
• Event semantics (A semantics for first-order logic wherein one declares predicates to be true in relation to some event or some action resulting from an event e.g. $Occurs(e,Alice,a)\wedge Walk(a,the\_dog)Quick(e)$ would mean "An event $e$ occurs wherein Alice does action $a$. Action $a$ is 'walk the dog'. The event is quick".