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Results tagged with surreal-numbers
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user 92164
For questions about the surreal numbers, which are a real-closed ordered proper-class-sized field that contains both the real numbers and the ordinal numbers. Thus they contain both infinite numbers (including the ordinals, but also infinite numbers like ω-1 and sqrt(ω)) and infinitesimal numbers (like 1/ω). They can also be identified with a subclass of two-player partisan games.
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Roots of $\omega$, larger $\gamma$-numbers
In Harry Gonshor's An Introduction to the Theory of Surreal Numbers, on page 50, Gonshor points to a method for intuitively guessing what the square root of the countable infinity is in his constructi …
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6
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answer
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Are the Surreals a cogenerator in the category of ordered fields?
A cogenerator in a category $\mathcal{C}$ is an object $\Omega$ such that for any pair of parallel arrows $f,g:X\rightrightarrows Y$ in $\mathcal{C}$ we have
$$
\forall h:Y\to\Omega\big(h\circ f=h\cir …
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answers
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Who discovered the surreals?
Common folklore dictates that the Surreals were discovered by John Conway as a lark while studying game theory in the early 1970's, and popularized by Donald Knuth in his 1974 novella.
Wikipedia disa …
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Factorization in the Omnific Integers
I'm wondering if there's been any work done on prime factorizations of Omnific integers as products of prime Omnific integers.
I suspect that each Omnific integer has a unique prime factorization, …
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3
votes
1
answer
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Functions on a field representable by Hahn series?
It is well known (see here for example) that a function over $\mathbb{R}$ is representable by a power series iff its analytic continuation to $\mathbb{C}$ is holomorphic on some open subset of $\mathb …
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3
votes
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'Smallest' subfield of the Surreals which is isomorphic to the Surreals as an ordered group
What is the smallest subfield $F\subset N_0$ such that $$(F,+,\times,\leq)\ncong(N_0,+,\times,\leq)$$ but $$(F,+,\leq)\cong(N_0,+,\leq)?$$ Since these are all going to be proper classes cardinality is …
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The surreal numbers under a change of universe
Suppose we start with a model $\mathcal{M}$ of $ZFC$ (or $GBC$ or $MK$ if you prefer), and let $N_0^\mathcal{M}$ denote the surreals in $\mathcal{M}$. If we add some large cardinal assumptions $\{\ph …
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