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The American Mathematical Monthly, 1975
hItroduction. During the past decade, many new axioms of set theory have appeared. The principal object of these axioms is to settle important problems which cannot be settled without new axioms. Thus Godel and Cohen have shown that the Continuum Hypothesis cannot be settled on the basis of the presently accepted axioms; so it is natural to look for ...
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hItroduction. During the past decade, many new axioms of set theory have appeared. The principal object of these axioms is to settle important problems which cannot be settled without new axioms. Thus Godel and Cohen have shown that the Continuum Hypothesis cannot be settled on the basis of the presently accepted axioms; so it is natural to look for ...
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The Bounded Axiom A Forcing Axiom
Mathematical Logic Quarterly, 2010AbstractWe introduce the Bounded Axiom A Forcing Axiom (BAAFA). It turns out that it is equiconsistent with the existence of a regular ∑2‐correct cardinal and hence also equiconsistent with BPFA. Furthermore we show that, if consistent, it does not imply the Bounded Proper Forcing Axiom (BPFA) (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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Independent set axioms, base axioms and circuit axioms of\\ supermatroids
SCIENTIA SINICA Mathematica, 2016Dunstan et al. first proposed the concept of supermatroids in 1972 by generalizing the underlying sets of matroids from finite sets to finite posets. Barnabei et al. introduced another matroidal structure on posets, i.e., poset matroids. By the one-to-one correspondence between finite distributive lattices and finite posets, poset matroids are just ...
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Part VII - AXIOMS: the axioms of integrodynamics
This paper establishes the axiomatic foundations of Integrodynamics: the unified dynamical theory governing contradiction, symmetry, adaptation, and integrity across epistemic, procedural, and institutional systems. Building on the preceding six papersof the Integrity series, this work consolidates their implicit assumptions into a minimal and completeopenaire +1 more source
We propose a unified geometric framework in which the mass, spin, interactions, and curvature of spacetime emerge from the topological and dynamical properties of a fundamental torsion field \tau^\mu. In this model, all fundamental particles are described as quantized winding excitations of the torsion field, and the spontaneous breaking of torsional
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1992
AbstractPursues the theoretical level of the two‐tiered epistemology of set theoretic realism, the level at which more abstract axioms can be justified by their consequences at more intuitive levels. I outline the pre‐axiomatic development of set theory out of Cantor's researches, describe how axiomatization arose in the course of Zermelo's efforts to ...
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AbstractPursues the theoretical level of the two‐tiered epistemology of set theoretic realism, the level at which more abstract axioms can be justified by their consequences at more intuitive levels. I outline the pre‐axiomatic development of set theory out of Cantor's researches, describe how axiomatization arose in the course of Zermelo's efforts to ...
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