Transfinite induction

Known as: Transfinite iteration, Induction, Well-ordered induction 
Transfinite induction is an extension of mathematical induction to well-ordered sets, for example to sets of ordinal numbers or cardinal numbers. Let… (More)
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2015
2015
We study a transfinite construction we call tower construction in classical type theory. The construction is inductive and… (More)
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2011
2011
In this paper we discuss the recently introduced transfinite Knuth-Bendix orders. We prove that any such order with finite… (More)
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2008
2008
  • Z. Ratajczyk
  • 2008
We generalize to the case of arithmetical transfinite induction the following three theorems for PA: the Wainer Theorem, the… (More)
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2005
2005
We apply Mints’ technique for proving the termination of the epsilon substitution method via cut-elimination to the system of… (More)
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2004
2004
1. Iterated Gödelian extensions of theories. The idea of iterating ad infinitum the operation of extending a theory T by adding… (More)
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1995
1995
The relative strengths of first-order theories axiomatized by transfinite induction, for ordinals less-than ~0, and formulas… (More)
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Highly Cited
1995
Highly Cited
1995
We establish some fundamental facts for infinitary orthogonal term rewriting systems (OTRSs): for strongly convergent reductions… (More)
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Highly Cited
1991
Highly Cited
1991
In this paper, a proof method based on a notion of transfinite semantic trees is presented and it is shown how to apply it to… (More)
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Highly Cited
1989
Highly Cited
1989
In the beginning of article we show some consequences of the regularity axiom. In the second part we introduce the successor of a… (More)
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1981
1981
In this paper we extend certain results of DE BARROS [1] on the subject of finite induction. We do this through the introduction… (More)
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