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person studying pure untyped lambda calculus, but at a simple level. I would really appreciate the input of lambda calculus mathematicians. I would like...

paradox#No_resolution_in_Lambda_Calculus. However I think a new page is needed discussing this issue, based on Curry's papers, called Deductive lambda calculus. I will...

semantics of untyped lambda calculus. One is the "domain" approach, explained (though not very clearly) in the linked Deductive lambda calculus article. In this...

March 2015 (UTC) Readers unfamiliar with lambda calculus should read the lambda calculus first! Lambda calculus is a prerequisite to understand the HM type...

Other kind of formal systems are Proof calculus, Formal ethics, Logical system, Lambda calculus, Propositional calculus The difference between a formal system...

understand what that buys us. I thought natural deduction was just the deductive calculus apparatus. Can someone explain to me why the "judgment," "evident...

first-order-logic: Barendregt, "The Lambda Calculus, Its syntax and semantics" defines theories and models for lambda calculus in pages 75-125. There is a very...

the formal system. A further example about expressions: simply-typed lambda-calculus is the term language of intuitionistic propositional logic. Hence proofs...

correspondence between simply typed lambda calculus and Cartesian closed categories, which entails defining a lambda-theory (pretty much the higher-order...

logical calculus, or a logical system) consists of a formal language together with a deductive apparatus (also called a deductive system). The deductive apparatus...

semantics, but there are many deductive systems, so it is common to look at a completeness proof as showing that a deductive system is complete with respect...

Russell never saw the light of day (he constructed a predecessor to the lambda calculus in his correspondence with Frege, and carried it to quite reasonable...

can be implemented with lambda calculus' abstraction operator λ {\displaystyle \lambda } etcetera . {\displaystyle .} (The lambda and the dot demarcate...

roots, a set of assumptions, such as set theory, peano arithmetic or lambda calculus. From any of these roots it was possible to derive the same theorems...

'fat' version of the predicate calculus provides likely opportunities for other unification versions and for other deductive operations. Refs::: [de Champeaux...

give an axiomisation for deductive systems based on first order logic, like Hilbert system, Natural deduction or Sequent calculus. These pages actually list...

sequential computation and some kinds of parallel computation including the lambda calculus. There is something wrong with the first sentence: is it Arbiters are...

formal systems that were known at the time [Post/Turing machines and lambda-calculus coming 5-6 years later] -- "in all the well-known formal systems of...

was proving that ℕ, etc. are computationally undecidable using the lambda calculus, which was published the next year. Of course, computational undecidabilty...

approaches that include (general) recursion, Turing machines, and the lambda calculus. In giving definitions based on these notions, we must not assume the...