Ax1. If p is a level then p is not above p Ax2. If each of P and Q is a level an

Question

Ax1. If p is a level then p is not above p

Ax2. If each of P and Q is a level and P is above Q, then there exists a level X such that P is above X and X is above Q

Ax3. if P and Q are levels then P is above Q or Q is above P

Ax4. If P, Q, and R are levels, and P is above Q and Q is above R, then P is above R

Ax5. If P is a level, then there exists levels x and y such that y is above P and P is above x.

Ax6. If S1 and S2 are level sets such that (1) if x is a level the x is in S1 or x is in S2 and (2) if x is a level in S1 and y is a level in S2 then y is above x, then S1 has a top level or S2 has a bottom level

Answer and prove your answer to the following statement

Question: Suppose A and B are levels and M is a level set whose only members areA and B. Are there any levels that are accumulation levels of M?

Explanation / Answer

Go through Ax6 as levels are above or below so accumulation is not possible. A is above B or below so every element has unique level

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