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Mass problems and measuretheoretic regularity
, 2009
"... Research supported by NSF grants DMS0600823 and DMS0652637. ..."
Abstract

Cited by 4 (3 self)
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Research supported by NSF grants DMS0600823 and DMS0652637.
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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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 ∈ X and ∀a(a ∈ X ⇒ f(a) ∈ X). The system A,i,f is said to be inductive if the only inductive subset of A is A itself. Define a Peano system to be an inductive system such that f is onetoone and i /∈ the range of f. The standard example of a Peano system is N,0,S where N = {0,1,2,...,n,...} = the set of natural numbers and S: N → N is given by S(n) = n+1 for all n ∈ N. Consider the statement that all Peano systems are isomorphic toN,0,S. We prove that this statement is logically equivalent to WKL0 over RCA ∗ 0. From this and similar equivalences we
and Shieva Kleinschmidt. Outline of this talk:
, 2009
"... Abstract: We present some ideas in furtherance of objectivity in mathematics. We call for closer integration of mathematics with the rest of human knowledge. We note some insights which can be drawn from current research programs in the foundations of mathematics. 1 First, a big thank you to Justin ..."
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Abstract: We present some ideas in furtherance of objectivity in mathematics. We call for closer integration of mathematics with the rest of human knowledge. We note some insights which can be drawn from current research programs in the foundations of mathematics. 1 First, a big thank you to Justin ClarkeDoane