I recently looked at Permutations on the random permutation which seems to talk about the notion of random permutuation as a notion from logic rather than probability.

The random permutation is the Fraïssé limit of the class of finite structures with two linear orders.

The intro also mentions that finite permutations are "two linear orders on a finite set".

I am not a logician, so I don't know what Fraïssé limit could be, but I got something about age in model theory.

There a sense in which a random permutation is a "universal" construction?

• http://math.stackexchange.com/questions/63150/what-is-a-universal-property

Is there a sense in which a "random" object can be a logical construction?

• Ed Nelson's Radically Elementary Probability Theory is a fascinating non-standard construction of law of large numbers and stochastic proceses, but I could not find an explanation of the random permutation.

I recently looked at Permutations on the random permutation which seems to talk about the notion of random permutuation as a notion from logic rather than probability.

The random permutation is the Fraïssé limit of the class of finite structures with two linear orders.

The intro also mentions that finite permutations are "two linear orders on a finite set".

I am not a logician, so I don't know what Fraïssé limit could be, but I got something about age in model theory.

There a sense in which a random permutation is a "universal" construction?

• https://math.stackexchange.com/questions/63150/what-is-a-universal-property

Is there a sense in which a "random" object can be a logical construction?

• Ed Nelson's Radically Elementary Probability Theory is a fascinating non-standard construction of law of large numbers and stochastic proceses, but I could not find an explanation of the random permutation.

I recently looked at Permutations on the random permutation which seems to talk about the notion of random permutuation as a notion from logic rather than probability.

The random permutation is the Fraïssé limit of the class of finite structures with two linear orders.

The intro also mentions that finite permutations are "two linear orders on a finite set".

I am not a logician, so I don't know what Fraïssé limit it, but I got something about age in model theory.

There a sense in which a random permutation is a "universal" construction?

• http://math.stackexchange.com/questions/63150/what-is-a-universal-property

Is there a sense in which a "random" object can be a logical construction?

• Ed Nelson's Radically Elementary Probability Theory is a fascinating non-standard construction of law of large numbers and stochastic proceses, but I could not find an explanation of the random permutation.

I recently looked at Permutations on the random permutation which seems to talk about the notion of random permutuation as a notion from logic rather than probability.

The random permutation is the Fraïssé limit of the class of finite structures with two linear orders.

The intro also mentions that finite permutations are "two linear orders on a finite set".

I am not a logician, so I don't know what Fraïssé limit could be, but I got something about age in model theory.

There a sense in which a random permutation is a "universal" construction?

• http://math.stackexchange.com/questions/63150/what-is-a-universal-property

Is there a sense in which a "random" object can be a logical construction?

• Ed Nelson's Radically Elementary Probability Theory is a fascinating non-standard construction of law of large numbers and stochastic proceses, but I could not find an explanation of the random permutation.