Archive for Mathematical Logic 30 (2):125-127 (1990)

Daniel M. Leivant
Indiana University, Bloomington
We consider HA*, that is Heyting's Arithmetic extended with transfinite induction over all recursive well orderings, which may be viewed as defining constructive truth, since PA* agrees with classical truth. We prove that Markov's Principle, as a schema, is not provable in HA*, but that HA* is closed under Markov's Rule.
Keywords Constructive arithmetic  Intuitionism  contrustive truth  Markov's Principle  Markov's Rule
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DOI 10.1007/BF01634982
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Proof Theory and Constructive Mathematics.Anne S. Troelstra - 1977 - In Jon Barwise & H. Jerome Keisler (eds.), Handbook of Mathematical Logic. North-Holland Pub. Co.. pp. 973--1052.
On the Consistency of Certain Logical Calculus.P. S. Novikoff - 1946 - Journal of Symbolic Logic 11 (4):129-131.

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