Continuity and Uncountability
in [Logic]
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From: Nam Nguyen on 7 Jul 2010 22:47 Would continuity and uncountability Suppose we a language L that has the ordinary semantics for the 2-ary predicate symbol '<'. We can't formalize the concept of continuity with a T (written in L) that has only countable models: the models must be at least of cardinality aleph_1. Now, however, part of continuity is discreteness. And so it begs the question, which is that: what's the concept which would require the models be of at least aleph_2 and of which continuity would be a part like, again, discreteness is a part of continuity? -- ---------------------------------------------------- There is no remainder in the mathematics of infinity. NYOGEN SENZAKI ----------------------------------------------------
From: Nam Nguyen on 7 Jul 2010 22:50
Nam Nguyen wrote: > > Would continuity and uncountability (Please disregard the above. It was unintended.) > > Suppose we a language L that has the ordinary semantics for > the 2-ary predicate symbol '<'. We can't formalize the concept > of continuity with a T (written in L) that has only countable > models: the models must be at least of cardinality aleph_1. > > Now, however, part of continuity is discreteness. And so it > begs the question, which is that: what's the concept which > would require the models be of at least aleph_2 and of which > continuity would be a part like, again, discreteness > is a part of continuity? -- ---------------------------------------------------- There is no remainder in the mathematics of infinity. NYOGEN SENZAKI ---------------------------------------------------- |