Pitowsky's Kolmogorovian Models and Super-determinism.

Area of Science:

• Foundations of Physics
• Mathematical Physics
• Set Theory

Background:

• Exploration of local hidden variables in quantum mechanics.
• Pitowsky's construction of "spin-[Formula: see text] functions" and "Kolmogorovian models" using nonstandard probability.
• The role of set theory axioms, like the Continuum Hypothesis, in physical models.

Purpose of the Study:

• To analyze Pitowsky's mathematical constructions for local hidden variables.
• To critically evaluate the physical relevance of Pitowsky's models.
• To connect the use of advanced set theory in physics to broader interpretational principles.

Main Methods:

• Description and analysis of Pitowsky's "spin-[Formula: see text] functions" and "Kolmogorovian models".
• Reinterpretation of Pitowsky's hidden variable approach as super-determinism.
• Philosophical argument regarding the physical relevance of non-measurable functions and set theory axioms.

Main Results:

• Pitowsky's models, intended to show mathematical possibility of local hidden variables, are identified as super-determinism.
• Super-determinism is deemed physically irrelevant in the context of quantum foundations.
• The use of the Continuum Hypothesis in Pitowsky's work is interpreted as supporting the irrelevance of non-measurable functions in physics.

Conclusions:

• Pitowsky's mathematical constructions do not support physically relevant local hidden variables.
• The study reinforces the principle that constructs requiring non-measurable functions are likely physically irrelevant.
• The debate on set theory axioms in physics is reframed by the physical irrelevance of the specific mathematical tools employed.