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Tagged with foundations-of-mathematics axiom
5 questions
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Does set-theoretic pluralism, about axiom systems, inevitably become an invitation to non-axiomatic systems of set theory?
Per Hamkins[[11][12]] (see also his [22]), if no individual axiom is too sacred to be denied in some possible world,Q and so if no collection of such axioms is so sacred either, yet then:
The ...
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What are the First Principles of Euclidean Geometry (Besides the Axioms)?
On first principles, Wikipedia says:
A first principle is an axiom that cannot be deduced from any other within that system. The classic example is that of Euclid's Elements; its hundreds of ...
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What is the current status of Foundation-of-Mathematics programmes?
I have been reading 'A Very Short Introduction to Mathematics' by Timothy Gowers and at one point he mentions that most of the mathematical proofs can be finally resolved to a set of logical ...
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Is it possible to create an axiomatic system where 1+1 doesn't equal 2? What would be the consequences of such a system? [closed]
1+1=2 is a result (perhaps arguably more of a definition than a theorem?) of Peano Arithmetic, as well as other systems such as ZFC. I understand that 1+1 doesn't necessarily have to equal 2 if we ...
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Is there an infinity of axioms in mathematics?
As I was trying to find a list of mathematical axioms used in modern branches of mathematics, I wondered if there's any meaning to the question of "how many mathematical axioms are there ?", and then ...
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