This essay shows how the forcing relation with underlying logic \(X\) might be represented in a way which more closely resembles an axiomatic approach. Following the initial result we take up the case of representing the forcing relation in which the underlying logic \(X\) allows sets on the the right of \( \vdash_X \). This requires us to redefine the notion of \(X\)-level forcing to take into account the 'handedness' of sets. We must also expand the definition of \(X\)-level to take this diffe…
Read moreThis essay shows how the forcing relation with underlying logic \(X\) might be represented in a way which more closely resembles an axiomatic approach. Following the initial result we take up the case of representing the forcing relation in which the underlying logic \(X\) allows sets on the the right of \( \vdash_X \). This requires us to redefine the notion of \(X\)-level forcing to take into account the 'handedness' of sets. We must also expand the definition of \(X\)-level to take this difference into account.
