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JSYML
2010
89views more  JSYML 2010»
13 years 2 months ago
The consistency strength of choiceless failures of SCH
We determine exact consistency strengths for various failures of the Singular Cardinals Hypothesis (SCH) in the setting of the Zermelo-Fraenkel axiom system ZF without the Axiom o...
Arthur W. Apter, Peter Koepke
WINE
2010
Springer
144views Economy» more  WINE 2010»
13 years 5 months ago
An Axiomatic Characterization of Continuous-Outcome Market Makers
Abstract. Most existing market maker mechanisms for prediction markets are designed for events with a finite number of outcomes. All known attempts on designing market makers for f...
Xi Alice Gao, Yiling Chen
CADE
2006
Springer
14 years 7 months ago
Extracting Programs from Constructive HOL Proofs Via IZF Set-Theoretic Semantics
Church's Higher Order Logic is a basis for proof assistants -- HOL and PVS. Church's logic has a simple set-theoretic semantics, making it trustworthy and extensible. We ...
Robert L. Constable, Wojciech Moczydlowski
MLQ
2010
226views more  MLQ 2010»
13 years 5 months ago
The Ultrafilter Closure in ZF
: It is well known that, in a topological space, the open sets can be characterized using filter convergence. In ZF (Zermelo-Fraenkel set theory without the Axiom of Choice), we c...
Gonçalo Gutierres
CADE
2006
Springer
14 years 7 months ago
On the Strength of Proof-Irrelevant Type Theories
We present a type theory with some proof-irrelevance built into the conversion rule. We argue that this feature is useful when type theory is used as the logical formalism underlyi...
Benjamin Werner