×

zbMATH — the first resource for mathematics

A completeness proof for adapted probability logic. (English) Zbl 0601.03004
Adapted probability logic is a formal logic appropriate for the study of continuous time stochastic processes. It was introduced by Keisler, and has been developed by Keisler and Hoover and others. This paper provides a short and clear completeness proof for this logic.
Reviewer: H.E.Kyburg

MSC:
03B48 Probability and inductive logic
60A05 Axioms; other general questions in probability
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] S. Fajardo, Completeness theorems for the general theory of processes, Proc. Sixth Latin American Logic Conference, to appear. · Zbl 0595.03014
[2] Hoover, D., Probability logic, Ann. math. logic, 14, 282-313, (1978) · Zbl 0394.03033
[3] Hoover, D.; Keisler, H.J., Adapted probability distributions, Trans. amer. math. soc., 286, 159-201, (1984) · Zbl 0548.60019
[4] Keisler, H.J., Hyperfinite probability theory and probability logic, () · Zbl 0167.01403
[5] Keisler, H.J., Probability quantifiers, chapter 14, (), 509-556
[6] Keisler, H.J., Model theory for infinitary logic, (), x + 208
[7] Keisler, H.J., Hyperfinite models of adapted probability logic, Ann. pure appl. logic, 31, 71-86, (1986) · Zbl 0601.03005
[8] Loeb, P.A., Conversion from standard to non-standard measure spaces and applications in probability theory, Trans. amer. math. soc., 211, 113-122, (1975) · Zbl 0312.28004
[9] Loeb, P.A., A functional approach to nonstandard measure theory, (), 251-261 · Zbl 0533.28008
[10] Rodenhausen, H., The completeness theorem for adapted probability logic, (), Heidelberg
[11] Rodenhausen, H., A characterization of nonstandard liftings of measurable functions and stochastic processes, Israel J. math., 43, 1-22, (1982) · Zbl 0504.60003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.