Wikipedia:Requested articles/Mathematical Logic Source: en.wikipedia.org/wiki/Wikipedia:Requested_articles/Mathematical_Logic

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Model theory, proof theory, and recursion theory

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

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.

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Computational verb logic
Countable language
First-degree entailment
Nominal logic - perhaps related to Nominal terms (computer science) and Nominal techniques, see also [1]
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".