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Phish

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Phish Phish em performance no Alpine Valley, em East Troy, Wisconsin, em julho de 2003. Da direita para a esquerda: Page McConnell, Trey Anastasio, Jon Fishman e Mike Gordon. Informação geral Origem Burlington, Vermont País  Estados Unidos Gênero(s) Rock alternativo, jazz fusion, neo-psicodelia [ 1 ] Período em atividade 1983–2000 (hiatos) 2002–2004 2009–presente Gravadora(s) Elektra, Rhino/WMG, JEMP Integrantes Trey Anastasio Mike Gordon Jon Fishman Page McConnell Ex-integrantes Jeff Holdsworth Marc Daubert Página oficial Phish.com ...

Prove that all algebraic numbers are included in any elementary substructure of $mathbb R$

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4 $begingroup$ Let $A$ be an elementary substructure of $mathbb R$ where $mathbb R$ is $langle mathbb R,+,cdot,0,1rangle$ . Show that $A$ contains any algebraic number. What I tried to do was use the fact that if $a$ is an algebraic number than there exist some polynomial $p(x)$ such that $p(a)=0$ . There exist a formula $phi=exists{x}(x_ncdot x^n+ldots+x_0=0)$ That is both true in $mathbb R$ and in $A$ and thus there exists a number in $bin{A}$ that solves the polynomial. The problem is that I don't know if this number is $a$ or how to change the formula so that the number will be $a$ . logic algebraic-number-theory model-theory share | cite | improve this question ...