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Set Something Related To Martins Axiom And The Continuum Hypothesis Forcing

1	Set
2	Something Related To Martins Axiom And The Continuum Hypothesis
2	Forcing

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Equivalence Of Forcing Notions

Let and be two forcing notions such that given any generic subset of there is a generic subset of with $\mathfrak{M}[G]=\mathfrak{M}[H]$ and vice-versa. Then and are equivalent.

Since if $G\in\mathfrak{M}[H]$ , $\tau[G]\in\mathfrak{M}$ for any -name $\tau$ , it follows that if $G\in\mathfrak{M}[H]$ and $H\in\mathfrak{M}[G]$ then $\mathfrak{M}[G]=\mathfrak{M}[H]$ .