When I study the Bohm tree defined in The Lambda Calculus: Its Syntax and Semantics, H.P. Barendregt, Elseviser,$\cap\Phi$ or $\cup_i(M_i)$ always occurs. But I'm confused about the union and the intersection operation of Bohm trees. For example, $A=\{<<>, \lambda x.x>, <<0>, \bot>, <<1>, x>\}$ and $B=\{<<>, \lambda x.x>, <<0>, x>, <<1>, x>, <<0,0>, x>\}$; $A=\{<<>, \lambda xy.x>, <<0>, \bot>, <<1>, x>\}$ and $B=\{<<>, \lambda x.x>, <<0>, y>, <<1>, \bot>\}$; $A=\{<<>, \lambda xy.x>, <<0>, \bot>, <<1>, x>\}$ and $B=\{<<>, \lambda x.x>, <<0>, \bot>, <<1>, y>\}$; $A=\{<<>, \lambda x.x>, <<0>, \bot>, <<1>, \bot>\}$ and $B=\{<<>, \lambda x.x>, <<0>, \bot>, <<1>, \bot>, <<2>, \bot>\}$. What's the results after doing union or intersection $A$ and $B$?
2026-03-26 16:10:35.1774541435
Union and intersection of Bohm trees
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