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Amending Frege’s Grundgesetze der Arithmetik
, 2002
"... Frege’s Grundgesetze der Arithmetik is formally inconsistent. This system is, except for minor differences, secondorder logic together with an abstraction operator governed by Frege’s Axiom V. A few years ago, Richard Heck showed that the ramified predicative secondorder fragment of the Grundgeset ..."
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Frege’s Grundgesetze der Arithmetik is formally inconsistent. This system is, except for minor differences, secondorder logic together with an abstraction operator governed by Frege’s Axiom V. A few years ago, Richard Heck showed that the ramified predicative secondorder fragment of the Grundgesetze is consistent. In this paper, we show that the above fragment augmented with the axiom of reducibility for concepts true of only finitely many individuals is still consistent, and that elementary Peano arithmetic (and more) is interpretable in this extended system.
NonStandard Models of Arithmetic: a Philosophical and Historical perspective
, 2010
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What is mathematical logic? A survey
, 2005
"... This paper was presented at the First Indian Conference on Logic and its relationship with other disciplines, Mumbai, January 2005 ..."
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This paper was presented at the First Indian Conference on Logic and its relationship with other disciplines, Mumbai, January 2005
Samsara
, 2005
"... In order to answer the question of what logic may be like in this twentyfirst century we examine the history of logic. One thing that we see is a recurrence of ideas but the ideas change form, sometimes quite dramatically. We also see a simple idea getting developed so much that it becomes very ..."
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In order to answer the question of what logic may be like in this twentyfirst century we examine the history of logic. One thing that we see is a recurrence of ideas but the ideas change form, sometimes quite dramatically. We also see a simple idea getting developed so much that it becomes very complicated, or at least the source of very complicated ideas  and then disappears, to reemerge, perhaps, as a new idea.