| __Citations: Introduction to Metamathematics - Kleene (ResearchIndex)__ *(Site not responding. Last check: 2007-10-07)* |

| | ....**Kleene** s three valued logic [26, 24, 44] We require that #R#(a1, a i, a i 2, ak) undef for every relational symbol R. Logical connectives in **Kleene** s strong threevalued logic are the strongest regular extension of the corresponding connectives on the two valued domain |

| | **Stephen** Cole **Kleene** was the mathematician who saw most deeply into the nature of intuitionism, with his notion of recursive realizabilility; see [4] and |

| | I shall discuss realizability for formulas of arithmetic; the modifications necessary to discuss the free word algebra W are minor; for example, induction for W should be formulated as A x (ffl) 8x[A A x (0x) A x (1x) A: The function symbols are 0, S (successor) and Delta. |

| citeseer.ist.psu.edu /context/169070/0 (1750 words) |