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1,384
OPEN QUESTIONS IN REVERSE MATHEMATICS
, 2010
"... The objective of this paper is to provide a source of open questions in reverse mathematics and to point to areas where there could be interesting developments. The questions I discuss are mostly known and come from somewhere in the literature. My objective was to compile them in one place and discu ..."
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Cited by 8 (0 self)
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The objective of this paper is to provide a source of open questions in reverse mathematics and to point to areas where there could be interesting developments. The questions I discuss are mostly known and come from somewhere in the literature. My objective was to compile them in one place
Nonstandard Arithmetic and Reverse Mathematics
 Bulletin of Symbolic
"... Abstract. We show that each of the five basic theories of second order arithmetic that play a central role in reverse mathematics has a natural counterpart in the language of nonstandard arithmetic. In the earlier paper [HKK1984] we introduced saturation principles in nonstandard arithmetic which ar ..."
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Cited by 6 (1 self)
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Abstract. We show that each of the five basic theories of second order arithmetic that play a central role in reverse mathematics has a natural counterpart in the language of nonstandard arithmetic. In the earlier paper [HKK1984] we introduced saturation principles in nonstandard arithmetic which
Reverse mathematics of MF spaces
, 2006
"... This paper gives a formalization of general topology in second order arithmetic using countably based MF spaces. This formalization is used to study the reverse mathematics of general topology. For each poset P we let MF(P) denote the set of maximal filters on P endowed with the topology generated b ..."
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Cited by 11 (7 self)
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This paper gives a formalization of general topology in second order arithmetic using countably based MF spaces. This formalization is used to study the reverse mathematics of general topology. For each poset P we let MF(P) denote the set of maximal filters on P endowed with the topology generated
1 STRICT REVERSE MATHEMATICS Draft
, 2005
"... NOTE: This is an expanded version of my lecture at the special session on reverse mathematics, delivered at the Special Session on Reverse Mathematics held at the Atlanta AMS meeting, on January 6, 2005. TABLE OF CONTENTS ..."
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NOTE: This is an expanded version of my lecture at the special session on reverse mathematics, delivered at the Special Session on Reverse Mathematics held at the Atlanta AMS meeting, on January 6, 2005. TABLE OF CONTENTS
Computability, Reverse Mathematics and Combinatorics
, 2008
"... Mathematicians all know what it means to prove a theorem from some set of axioms. In Reverse Mathematics we reverse the process and study what axioms are actually required to prove a theorem. If we can omit some of the axioms and assume instead the “theorem” and use this to prove the omitted axioms ..."
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Mathematicians all know what it means to prove a theorem from some set of axioms. In Reverse Mathematics we reverse the process and study what axioms are actually required to prove a theorem. If we can omit some of the axioms and assume instead the “theorem” and use this to prove the omitted
Determinacy of Infinite and Reverse Mathematics
, 2009
"... This thesis consists of two parts. The first part treats determinacy in (classical) reverse mathematics and the second part treats determinacy in intuitionistic mathematics. The first part investigates the logical strength of the determinacy of infinite games in the Cantor space in terms of second o ..."
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This thesis consists of two parts. The first part treats determinacy in (classical) reverse mathematics and the second part treats determinacy in intuitionistic mathematics. The first part investigates the logical strength of the determinacy of infinite games in the Cantor space in terms of second
INTERVAL ORDERS AND REVERSE MATHEMATICS
, 2006
"... Abstract. We study the reverse mathematics of interval orders. We establish the logical strength of the implications between various definitions of the notion of interval order. We also consider the strength of different versions of the characterization theorem for interval orders: a partial order i ..."
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Cited by 1 (0 self)
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Abstract. We study the reverse mathematics of interval orders. We establish the logical strength of the implications between various definitions of the notion of interval order. We also consider the strength of different versions of the characterization theorem for interval orders: a partial order
Reverse mathematics and Peano categoricity
"... We investigate the reversemathematical status of several theorems to the effect that the natural number system is secondorder categorical. One of our results is as follows. Define a system to be a triple A,i,f such that A is a set and i ∈ A and f: A → A. A subset X ⊆ A is said to be inductive if i ..."
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Cited by 1 (0 self)
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We investigate the reversemathematical status of several theorems to the effect that the natural number system is secondorder categorical. One of our results is as follows. Define a system to be a triple A,i,f such that A is a set and i ∈ A and f: A → A. A subset X ⊆ A is said to be inductive
Reverse mathematics and fully ordered groups
, 2003
"... The fundamental question in reverse mathematics is to determine which set existence axioms are required to prove particular theorems of ordinary mathematics. In this case, we consider ..."
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Cited by 2 (2 self)
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The fundamental question in reverse mathematics is to determine which set existence axioms are required to prove particular theorems of ordinary mathematics. In this case, we consider
Reverse Mathematics and Recursive Graph Theory
 Math. Log. Quart
, 1998
"... Abstract. We examine a number of results of infinite combinatorics using the techniques of reverse mathematics. Our results are inspired by similar results in recursive combinatorics. Theorems included concern colorings of graphs and bounded graphs, Euler paths, and Hamilton paths. Reverse mathemati ..."
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Cited by 4 (1 self)
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Abstract. We examine a number of results of infinite combinatorics using the techniques of reverse mathematics. Our results are inspired by similar results in recursive combinatorics. Theorems included concern colorings of graphs and bounded graphs, Euler paths, and Hamilton paths. Reverse
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