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2. Stephen Cole Kleene - Wikipedia

   en.wikipedia.org/wiki/Stephen_Cole_Kleene

   Stephen Cole Kleene (/ ˈ k l eɪ n i / KLAY-nee; [a] January 5, 1909 – January 25, 1994) was an American mathematician.One of the students of Alonzo Church, Kleene, along with Rózsa Péter, Alan Turing, Emil Post, and others, is best known as a founder of the branch of mathematical logic known as recursion theory, which subsequently helped to provide the foundations of theoretical computer ...

3. Kleene algebra - Wikipedia

   en.wikipedia.org/wiki/Kleene_algebra

   In mathematics and theoretical computer science, a Kleene algebra (/ ˈ k l eɪ n i / KLAY-nee; named after Stephen Cole Kleene) is a semiring that generalizes the theory of regular expressions: it consists of a set supporting union (addition), concatenation (multiplication), and Kleene star operations subject to certain algebraic laws.

4. Metamathematics - Wikipedia

   en.wikipedia.org/wiki/Metamathematics

   Metamathematics provides "a rigorous mathematical technique for investigating a great variety of foundation problems for mathematics and logic" (Kleene 1952, p. 59). An important feature of metamathematics is its emphasis on differentiating between reasoning from inside a system and from outside a system.

5. Kleene's recursion theorem - Wikipedia

   en.wikipedia.org/wiki/Kleene's_recursion_theorem

   The sequence F k used in this proof corresponds to the Kleene chain in the proof of the Kleene fixed-point theorem. The second part of the first recursion theorem follows from the first part. The assumption that Φ is a recursive operator is used to show that the fixed point of Φ is the graph of a partial function.

6. Alonzo Church - Wikipedia

   en.wikipedia.org/wiki/Alonzo_Church

   Alonzo Church (June 14, 1903 – August 11, 1995) was an American computer scientist, mathematician, logician, and philosopher who made major contributions to mathematical logic and the foundations of theoretical computer science. [2]

7. Mathematical logic - Wikipedia

   en.wikipedia.org/wiki/Mathematical_logic

   Kleene's work with the proof theory of intuitionistic logic showed that constructive information can be recovered from intuitionistic proofs. For example, any provably total function in intuitionistic arithmetic is computable ; this is not true in classical theories of arithmetic such as Peano arithmetic .

8. Church–Turing thesis - Wikipedia

   en.wikipedia.org/wiki/Church–Turing_thesis

   The Church–Turing Thesis: Stephen Kleene, in Introduction To Metamathematics, finally goes on to formally name "Church's Thesis" and "Turing's Thesis", using his theory of recursive realizability. Kleene having switched from presenting his work in the terminology of Church-Kleene lambda definability, to that of Gödel-Kleene recursiveness ...

9. Kleene fixed-point theorem - Wikipedia

   en.wikipedia.org/wiki/Kleene_fixed-point_theorem

   In the mathematical areas of order and lattice theory, the Kleene fixed-point theorem, named after American mathematician Stephen Cole Kleene, states the following: Kleene Fixed-Point Theorem. Suppose ( L , ⊑ ) {\displaystyle (L,\sqsubseteq )} is a directed-complete partial order (dcpo) with a least element, and let f : L → L {\displaystyle ...