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2
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A fixed point problem in infinite dimensions for monotonic algebras

Let $A$ be an algebra over $[0,1]$, whose operations are all unary monotone (increasing or decreasing) bijections, except that $A$ also includes the infimum operation over finite or countably many ...
3
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2answers
403 views

Avoiding reflexive paradox in set theory

I am an amateur mathematician, and certainly not a set theorist, but there seems to me to be an easy way around the reflexive paradox: Add to set theory the primitive $A(x,y)$, which we may think of ...
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553 views

Positive results coming from paradoxes

Many examples comes to mind, the most famous being the Gödel's theorems viewed as formalisations of the Liar's paradox. I just realised that the proof of non-calculability of Kolmogorov complexity is ...
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5answers
905 views

How to tell a paradox from a “paradox”?

Russell's paradox showed that naive set theory leads to a contradiction. This was something that was taken seriously and caused a lot of work. Now, Banach–Tarski paradox is arises from a result that ...