https://math.codidact.com/categories/41/tags/3992.rssNew Posts Tagged 'set-theory' - MathematicsMathematics - Codidact2024-02-12T09:17:56Zhttps://math.codidact.com/posts/290742Concrete examples of set theorists thinking independence proofs only determine provability rather than that a statement is neither true nor false?Julius H.https://math.codidact.com/users/573372024-02-10T16:15:15Z2024-02-12T09:17:56Z<p>I’m curious to know more about this quote from a paper by Joel David Hamkins.</p>
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<p>The pervasive independence phenomenon in set theory is described on this view as a distraction...https://math.codidact.com/posts/290740What are the “increasingly stable consequences of the large cardinal hierarchy”?Julius H.https://math.codidact.com/users/573372024-02-10T15:35:55Z2024-02-10T15:35:55Z<p>I would like to understand the following quote, from a <a href="https://arxiv.org/abs/1108.4223">paper</a> by Joel Hamkins:</p>
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<p>Adherents of the universe view often point to th...https://math.codidact.com/posts/290727Defining Bayes’s theorem from scratch in ZFCJulius H.https://math.codidact.com/users/573372024-02-09T22:58:20Z2024-02-09T22:58:20Z<p>I have tons of interrelated questions which I would like resolved in order to help me answer this <a href="https://philosophy.stackexchange.com/a/108474/56485">Philosophy SE</a> question about B...https://math.codidact.com/posts/287720Proving $|{\bf R}^{\bf R}|=|2^{\bf R}|$ using the Schroeder-Bernstein TheoremSnoopyhttps://math.codidact.com/users/568172023-01-14T14:38:38Z2023-01-15T11:46:31Z<p>Let $A$ be the set of <em>all</em> functions from ${\bf R}$ to ${\bf R}$ and $B$ the power set of ${\bf R}$. Then $|A|=|B|$.</p>
<p>This is a well-known result in set theory. A quick search on ...https://math.codidact.com/posts/287269Is this formula for the minimal sum correct?celtschkhttps://math.codidact.com/users/80562022-10-16T09:13:41Z2022-11-06T11:06:36Z<p>As is well known, the addition of natural numbers can be extended to the ordinal numbers in different ways. The first way is the ordinal sum, and the second is the natural or Hessenberg sum.</p>...https://math.codidact.com/posts/284907Third kind of infiniteEstelahttps://math.codidact.com/users/533202021-11-17T23:05:04Z2021-11-20T06:33:03Z<p>The most known infinities are the cardinality of the set of natural numbers and the cardinality of the set of real numbers.</p>
<p>Provide examples of different infinities. In other words, of s...https://math.codidact.com/posts/278430Existence of a set of all setsMathPhysicshttps://math.codidact.com/users/532052020-10-09T08:44:55Z2020-10-10T16:55:08Z<p>Suppose that we have an axiomatic set theory having the following axiom:</p>
<p><strong>The Axiom Schema of Comprehension:</strong> Let $\mathbf{P}(x)$ be a property of $x$. For any set $A$, the...