Intrinsic value (finance)

In mathematics, and in particular model theory, a prime model is a model which is as simple as possible. Specifically, a model $P$ is prime if it admits an elementary embedding into any model $M$ to which it is elementarily equivalent (that is, into any model $M$ satisfying the same complete theory as $P$).

Cardinality

In contrast with the notion of saturated model, prime models are restricted to very specific cardinalities by the Löwenheim-Skolem theorem. If $L$ is a first-order language with cardinality $\kappa$ and $T$ a complete theory over $L,$ then this theorem guarantees a model for $T$ of cardinality $\max (\kappa ,{\mathrm{\aleph }}_0);$ therefore no prime model of $T$ can have larger cardinality since at the very least it must be elementarily embedded in such a model. This still leaves much ambiguity in the actual cardinality. In the case of countable languages, all prime models are at most countable.

Relationship with saturated models

There is a duality between the definitions of prime and saturated models. Half of this duality is discussed in the article on saturated models, while the other half is as follows. While a saturated model realizes as many types as possible, a prime model realizes as few as possible: it is an atomic model, realizing only the types which cannot be omitted and omitting the remainder. This may be interpreted in the sense that a prime model admits "no frills": any characteristic of a model which is optional is ignored in it.

For example, the model $⟨\mathbb{\mathbb{N}},S⟩$ is a prime model of the theory of the natural numbers N with a successor operation S; a non-prime model might be $⟨\mathbb{\mathbb{N}}+\mathbb{\mathbb{Z}},S⟩,$ meaning that there is a copy of the full integers which lies disjoint from the original copy of the natural numbers within this model; in this add-on, arithmetic works as usual. These models are elementarily equivalent; their theory admits the following axiomatization (verbally):

1. There is a unique element which is not the successor of any element;
2. No two distinct elements have the same successor;
3. No element satisfies Sⁿ(x) = x with n>0.

These are, in fact, two of Peano's axioms, while the third follows from the first by induction (another of Peano's axioms). Any model of this theory consists of disjoint copies of the full integers in addition to the natural numbers, since once one generates a submodel from 0 all remaining points admit both predecessors and successors indefinitely. This is the outline of a proof that $⟨\mathbb{\mathbb{N}},S⟩$ is a prime model.

References

• Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
  
  Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
  
  In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
  
  Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
  
  Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
  
  15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
  
  To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010