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Consistency, Truth and Existence

  • Pavel Pudlák
Chapter
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Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

In the first section we mention the main philosophical approaches in the standard classification: platonism, intuitionism, logicism and formalism. In the second section, we discuss consistency statements, reflection principles and theories obtained by transfinite iterations of these principles. Furthermore, we present some results of the program of using large cardinals to cope with incompleteness in set theory. In the final section, we present the concept of physical natural numbers and attempt to give an alternative formalization of this concept.

Keywords

Natural Number Large Cardinal Peano Arithmetic Incompleteness Theorem Reflection Principle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Pavel Pudlák
    • 1
  1. 1.ASCRPragueCzech Republic

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