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jdh.hamkins.org | ||
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xorshammer.com
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| | | | | Let $latex \mathrm{PA}$ be Peano Arithmetic. Gödel's Second Incompleteness Theorem says that no consistent theory $latex T$ extending $latex \mathrm{PA}$ can prove its own consistency. (I'll write $latex \mathrm{Con}(T)$ for the statement asserting $latex T$'s consistency; more on this later.) In particular, $latex \mathrm{PA} + \mathrm{Con}(\mathrm{PA})$ is stronger than $latex \mathrm{PA}$. But certainly, given that... | |
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nickdrozd.github.io
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| | | | | The classic Busy Beaver function is defined as the maximum number of steps that an N-state 2-color Turing machine program can run before halting when started on the blank tape. The function is uncomputable, and any sound proof system S can only prove values up to a certain point. That is, there is some number Q such that | |
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jeremykun.wordpress.com
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| | | | | We assume the reader is familiar with the concepts of determinism and finite automata, or has read the corresponding primer on this blog. The Mother of All Computers Last time we saw some models for computation, and saw in turn how limited they were. Now, we open Pandrora's hard drive: Definition: A Turing machineis a... | |
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degoes.net
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| | | Functional programming has a bit of jargon, but that doesn't have to stop you from understanding core concepts | ||
